the Descent of Glaciers by their Weight only. 139 



done me the honour to reply to them. I am desirous to acknow- 

 ledge the courtesy with which the controversy has been conducted 

 by my opponents. Mr. Croll has done me the justice, I think, to 

 follow out the mathematical reasoning on which my argument is 

 based ; and I will not complain if Mr. Ball has not. Mr. Croll 

 accepts that one of my two conclusions which is the subject of my 

 present paper. He concedes that " if the ice of a glacier be in the 

 hard, solid, crystalline state in which it is generally admitted to 

 be, and its particles shear in that state as they are assumed to do, 

 then glaciers cannot possibly descend by their weight only, as 

 is generally supposed, and the generally received theory of gla- 

 cier-motion must be abandoned "*. Mr. Matthews, Mr. Ball, 

 and M. Heim dissent from this conclusion. I propose to answer 

 their objections to it in this paper, and in a subsequent one 

 those they have made specially to my own theory of the descent 

 of glaciers. 



The impossibility of the descent of glaciers by their weight 

 only, results from the consideration that, besides the motion of 

 the translation of a glacier bodily on its bed, there is a constant 

 displacement of its particles over one another and alongside 

 one another; for which displacement the work of a far more 

 ■powerful force is necessary than the weight of the glacier would 

 supply, it being subject (by the principles of mechanical philo- 

 sophy) to the condition that the aggregate work of the forces 

 which cause it must not be less than that of the resistances which 

 are opposed to it. 



It is, of course, impossible to represent this inequality mathe- 

 matically in respect to a glacier having a variable direction and 

 an irregular channel and slope ; but in respect to an imaginary 

 one, having a constant direction and a uuiform channel and slope, 

 it is possible. I have computed it numerically in respect to a 

 glacier of a uniform rectangular section, slope, direction, and 

 roughness, descending with the same velocity as the "Mer de 

 Glace " does, and I have found that the work done by the weight 

 of the glacier in such descent through any distance is only 

 about jjth of the work necessary to overcome the resistances 

 opposed to its descent through that distance. 



The weight of this imaginary glacier would therefore be far 

 too small a force to cause it to descend as glaciers do descend. 



The imaginary case to which my computation applies differs 

 from the case of the actual glacier in this respect, that the actual 

 glacier is not straight or of a uniform section and slope, and its 

 channel is not of a uniform roughness. 



In all these respects the resistance to the descent of the actual 

 glacier is greater than to that of the imaginary one. But this being 

 * Phil. Mag. S. 4. vol. xl. p. 154. 



